Fog boundary layer parameterization scheme correction method based on multi-scale physical coupling network

Abstract

The invention discloses a fog boundary layer parameterization scheme correction method based on a multi-scale physical coupling network, relates to the crossing field of numerical weather forecast and artificial intelligence, and aims to improve the performance of different boundary layer parameterization schemes in a WRF mode, construct a fusion framework of a physical mode and deep learning, adopt a double-branch heterogeneous network structure, and improve the performance of a fog boundary layer parameterization scheme. Establishing a nonlinear mapping relation between different parameterization scheme deviations and large eddy simulation turbulence characteristics by combining a space-time attention mechanism; by correcting systematic deviation existing in a parameterization scheme, the analysis capability of a turbulence structure is improved, and physical description of a boundary layer process is optimized; compared with a traditional boundary layer scheme, the method has the advantages that the fog zone simulation precision is remarkably improved, the fog zone visibility, the liquid water content and the root-mean-square error of a liquid water path are reduced by 66.7%, 50% and 58.3% respectively, the problem that turbulence intermittent characterization is insufficient under a stable boundary layer in a traditional method is effectively solved, and a new normal form is provided for refined forecasting of the fog generation and elimination process.

Description

Technical Field

[0001] The present invention relates to the intersection of numerical weather forecasting and artificial intelligence, and in particular to a method for correcting a fog boundary layer parameterization scheme based on a multi-scale physical coupling network. Background Art

[0002] The boundary layer parameterization scheme is a core component of the numerical weather forecast model, which directly affects the simulation accuracy of turbulent mixing, cloud microphysical processes and radiation effects. In the simulation of fog areas, especially under stable boundary layer conditions, the existing classical boundary layer schemes (such as YSU, ACM2, and QNSE schemes) mostly rely on local K theory or first-order closed turbulence assumptions, and assume that the turbulence statistics are linearly related to the average gradient. However, atmospheric turbulence exhibits obvious intermittent, non-local transmission and anisotropic characteristics. These traditional turbulence parameterization assumptions are difficult to accurately characterize the actual process, resulting in weak simulation of the top structure of the inversion layer, low cooling rate, loss of turbulent intermittent burst process, underestimated nighttime turbulent kinetic energy, delayed simulation of liquid water condensation and evaporation process, increased prediction error of fog top height, drastic changes in visibility, but slow or distorted model response.

[0003] Taking radiation fog as an example, the formation of fog depends on the coordinated evolution of surface radiation cooling and turbulence weakening, but the traditional scheme does not adequately characterize the radiation-turbulence coupling process. It only uses a simple stability function to correct the turbulence exchange coefficient, which cannot dynamically respond to changes in the local cooling rate, making it difficult to reproduce the actual fog generation and dissipation sequence. In addition, under complex terrain conditions (such as basins, canyons, and mountains), the thermally driven circulation caused by the terrain (such as valley winds and slope winds) and the local turbulence enhancement effect further aggravate the heterogeneity and non-stationarity of the boundary layer structure. Traditional parameterization schemes can maintain a certain degree of accuracy under simple terrain conditions, but the prediction error is significantly amplified under complex terrain, manifested in problems such as small fog area coverage, underestimated fog top height, and early or delayed life cycle prediction. In response to the limitations of the above physical schemes, researchers have proposed methods such as introducing high-order turbulence closure, local / non-local mixed correction terms, and turbulent energy spectrum parameterization to improve model accuracy. However, there are still shortcomings such as strong parameter dependence, sensitivity to initial fields and parameter selection, difficulty in ensuring physical consistency, increased computing costs, and reduced real-time business application capabilities of NWP systems. Limited by a priori physical assumptions, performance degrades significantly under extremely stable or local radiation cooling conditions.

[0004] In recent years, data assimilation techniques have been introduced to improve the output of initial fields and parameterization schemes. However, they rely on high-quality observational data and have limited effectiveness in data-sparse regions. With the rise of deep learning in the meteorological field, parameterization correction methods based on neural networks have gradually attracted attention. However, existing deep learning models still have deficiencies in multi-scale feature extraction, spatio-temporal dependence modeling, and physical constraint fusion. Especially in the simulation of fog in complex terrain areas, the generalization ability and accuracy of the models are limited. Therefore, there is an urgent need for a deep learning method that can effectively extract multi-scale spatio-temporal features, fuse physical constraints, and improve the accuracy of fog simulation. Summary of the Invention

[0005] To overcome the deficiencies of traditional boundary layer parameterization schemes in fog simulation, the present invention proposes a correction method for fog boundary layer parameterization schemes based on a multi-scale physical coupling network to solve the problem of insufficient accuracy in fog simulation by existing boundary layer parameterization schemes under stable conditions.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A correction method for fog boundary layer parameterization schemes based on a multi-scale physical coupling network, comprising the following steps:

[0008] S1. Use the numerical weather prediction model WRF to generate multi-parameterization boundary layer simulation data, and the input data includes thermodynamic variables, water substance variables, and dynamic field variables;

[0009] S2. Generate an initial feature tensor by feature encoding processing of the input data, and use the multi-head attention mechanism to screen out key variables with relatively large weights for the evolution of the fog area;

[0010] S3. Construct a multi-scale physical coupling network SMAP-Net, and respectively extract temperature and humidity phase state features and cloud water phase state features at different scales through a double-branch heterogeneous network structure;

[0011] S4. Fuse the features of the double branches through the spatio-temporal coupling attention module ST-CAM, and perform joint modeling of the non-linear relationships of turbulence, radiation, and phase change by using three-dimensional convolutional spatio-temporal encoding, bidirectional GRU time series modeling, and dynamic attention weighting;

[0012] S5. Embed a physical constraint loss function in the decoding stage, including the mass-momentum conservation equation and the visibility gradient matching term, and perform collaborative optimization of data-driven features and physical laws through adaptive weight allocation to correct boundary layer variables;

[0013] S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content, and visibility, to improve the simulation accuracy of the liquid water path LWP and liquid water content LWC in the fog area.

[0014] As a further preferred solution of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S2, the specific implementation of the encoding stage includes:

[0015] S2.1. The input variables include temperature T, relative humidity RH, water vapor mixing ratio Qv, cloud water content Qc, rain water content Qr, ice crystal content Qi, snow content Qs, air pressure P, and vertical velocity W. The input data is organized into a three-dimensional spatio-temporal tensor with dimensions H×W×T×C, where H×W represents the spatial resolution, T represents the time step, and C represents the number of variable channels;

[0016] S2.2. Extract spatio-temporal local features through a parallel three-dimensional convolutional layer. The convolutional kernel size of the three-dimensional convolutional layer is 3×3×3, the stride is 1, and the padding is 1; generate an initial feature tensor , where represents the number of output channels, and use the ReLU activation function for non-linear transformation;

[0017] S2.3. Use the multi-head attention mechanism to screen the initial feature tensor , and the calculation formula is as follows: Among them, , , are the query, key, and value vectors respectively, is a learnable linear transformation matrix. Each matrix is responsible for linearly transforming the channel dimension of the input feature tensor , keeping the dimension unchanged and continuously updated during the training process to optimize the attention calculation, realize the re-weighting of information between channels and the feature subspace mapping, so that different variable combinations can adapt to the subsequent correlation modeling, is the dimension of the key vector, and the attention mechanism is configured as heads, where is an adjustable hyperparameter, and the filtered feature tensor is output to highlight the key variables that have a greater impact on the evolution of the fog area.

[0018] As a further preferred solution of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S3, the specific implementation of the temperature and humidity phase branch includes:

[0019] S3.1. The input variables are temperature T, relative humidity RH, water vapor mixing ratio Qv, and air pressure P. Extract spatio-temporal local features through three-dimensional convolution. The convolutional kernel size of the three-dimensional convolution is 3×3×3, the stride is 1, and the padding is 1, and generate an initial feature tensor , where the number of output channels is 64;

[0020] S3.2. Adopt a 4-level Dense Block stacking structure, with each level containing a bottleneck structure. The bottleneck structure sequentially includes: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, and 1×1×1 convolution for dimensionality increase. The features of the previous layer and the current layer are concatenated in channels through skip connections, and a feature tensor is output. , where the number of output channels is 4×64 = 256 to enhance the feature reuse ability;

[0021] S3.3. Enhance the feature response of the inversion layer top and the humidity jump region through the channel-spatiotemporal hybrid attention CSTA mechanism. The calculation formula is as follows: Where, represents the global average pooling result along the spatial-temporal dimension, is a learnable weight matrix used to model the dependencies between channels, is the Sigmoid activation function to generate the channel attention weights, represents element-wise multiplication, is the output feature tensor of the Dense Block. The addition operation retains the original feature information, and an enhanced feature tensor is output. .

[0022] As a further preferred solution of the method for correcting the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, in step S3, the U-Transformer module of the cloud water phase branch includes:

[0023] S3.4. The input variables are cloud water content Qc, rain water content Qr, ice crystal content Qi, and snow content Qs. Multi-scale features are extracted through a U-shaped encoding-decoding structure. The input data dimension is H×W×T×4, where the number of channels is 4;

[0024] S3.5. The encoder adopts 2-level downsampling and combines a multi-scale adaptive position encoding MSPE block layer. Let the original three-dimensional coordinates of each position point be , where , are spatial coordinates, is the time index. For each dimension , different scale sets are selected, where is a positive integer used to control the number of frequency resolution levels of the encoding. Calculate the absolute position encoding: Where, is the coordinate in the dimension component, is the single-dimensional encoding vector. Concatenate the encoding vectors of each dimension: Where, For the complete absolute position encoding, for each scale introduce learnable weights , used to adjust the importance of features at different scales; for any two positions in the attention calculation and , calculate the coordinate difference: Map the coordinate difference to the relative position encoding through a lightweight MLP:

[0025] This relative position encoding has the same dimension as the hidden dimension of the MSPE block. In each MSPE block layer, add the absolute position encoding of each position to the input features after linear mapping, and use the relative position encoding as the bias term for attention weight calculation, used to adjust the attention intensity between different positions, thereby enhancing the modeling ability of multi-scale spatio-temporal relationships;

[0026] S3.6. The decoder uses a 3×3×3 convolutional kernel with a stride of 2 and skip connections through 2-level upsampling to fuse low-level local features and high-level semantic information, and outputs a multi-scale cloud water phase state feature tensor .

[0027] As a further preferred solution of the fog boundary layer parameterization scheme correction method based on the multi-scale physical coupling network of the present invention, in step S4, the implementation of the spatio-temporal coupling attention module ST-CAM includes:

[0028] S4.1. The input feature tensor is the output of the temperature-humidity phase state branch and the cloud water phase state branch, with a dimension of H×W×T×C. Build a multi-resolution feature pyramid using 3D convolutional kernels with dilation rates of 1, 2, and 4 respectively. The size of the 3D convolutional kernel is 3×3×3, the stride is 1, and the padding is same. The output feature channel numbers are respectively set to , , , where < < , to achieve the dimension increase operation, and fuse the features of the three scales into a unified feature tensor through a 1×1×1 convolutional layer , whose channel number is , to expand the model receptive field and capture the multi-scale spatio-temporal evolution pattern, and improve the modeling ability of fog area boundary layer variables;

[0029] S4.2. Model the lag effect of the development of the inversion layer along the time axis through a bidirectional GRU. The input feature tensor is unfolded into a sequence along the time axis The bidirectional GRU contains 2 layers, with the hidden state dimension of each layer being 128, the activation function being tanh, and the hidden state update formula being: , Among them, is the update gate, is the reset gate, , , , , , are learnable weight matrices, , , are bias terms, is the Sigmoid activation function, is the element-wise multiplication, is the unidirectional hidden state, and the bidirectional GRU generates the final hidden state through forward and backward calculations , enhancing the ability of temporal dynamic modeling;

[0030] S4.3. Calculate the correlation weights between grid points using the spatial self-attention mechanism to generate a dynamic attention map, and the calculation formula is as follows: Among them, SA represents the spatial attention mechanism, which is used to calculate the attention weights based on the feature similarity between grid points, , , are the query, key, and value vectors respectively, , , are linear transformation matrices, and each matrix linearly transforms the number of channels of the input , keeping the number of channels unchanged, and re-encoding the semantic representations of each grid point in different feature subspaces to provide an adapted feature subspace mapping for subsequent attention score calculation, is the key vector dimension, outputting the attention-weighted feature tensor, and then multiplying it element-wise with to generate the final fused feature tensor .

[0031] As a further preferred solution of the fog boundary layer parameterization scheme correction method based on the multi-scale physical coupling network of the present invention, in step S5, the physical constraint loss function includes:

[0032] S5.1. The pixel-level reconstruction loss uses the weighted mean square error (WMSE) to constrain the consistency between the correction field and the large eddy simulation (LES) data, and is defined as: Among them, represents the predicted correction field of the correction model SMAP-Net at the position ( ), is the true value for LES simulation, is the dynamic weight, and the calculation formula is: where, is the location of the terrain height, is the fog top height, is the standard deviation. The weight design weights the deviation between the terrain height and the fog top height in the form of a Gaussian function, thereby enhancing the error constraint of the key layer near the fog top in the loss function and improving the simulation accuracy of the key area;

[0033] S5.2. The mass-momentum conservation term strengthens the physical self-consistency by minimizing the residual of the Navier-Stokes equation and is defined as: where, is the air density, is the three-dimensional wind speed vector, is the air pressure, is the gravitational acceleration, represents the divergence of the mass flux and is used to constrain the continuity equation, represents the material derivative of the wind speed, represents the balance relationship between the inertial force, the pressure gradient force, and the gravity in the momentum conservation, , are hyperparameters for adjusting the weights of the two terms and are obtained through grid search and cross-validation;

[0034] S5.3. The visibility gradient matching term uses a contrastive loss function to maximize the similarity between the visibility feature and the surface temperature feature to enhance the sensitivity of the model to radiative cooling and fog layer changes. This loss function is defined as: where, is the feature vector of the visibility field, is the feature vector of the surface temperature field, is the negative sample feature vector, is the cosine similarity function, is the temperature parameter. The feature vectors are extracted by a three-layer convolutional neural network CNN. Each layer uses a fixed-size 3×3 convolutional kernel, and the number of output channels increases layer by layer to capture different levels of spatial patterns and semantic information;

[0035] S5.4. The total loss function is the weighted sum of each part: where, and are adaptive weight parameters and are dynamically optimized by a small multi-layer perceptron MLP; MLP contains two fully connected layers. The input is the of the current training epoch, , , and the output is and , the optimization objective is to minimize the prediction error on the validation set.

[0036] As a further preferred solution of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention, it includes the SMAP-Net model, and the SMAP-Net model includes a dual-branch feature extraction module, a spatio-temporal coupling attention module, and a physical constraint loss function module;

[0037] The dual-branch feature extraction module extracts the temperature-humidity phase state features and the cloud-water phase state features respectively through a dual-branch heterogeneous network structure. Among them, the temperature-humidity phase state branch uses the Dense Block and CSTA mechanisms to capture the multi-scale features of temperature and humidity, and the cloud-water phase state branch uses the U-Transformer module to extract the spatial distribution features of the cloud-water content;

[0038] The spatio-temporal coupling attention module fuses the dual-branch features output by the multi-scale physical coupling network module, performs spatio-temporal encoding using 3D convolution, models the temporal dependence relationship through bidirectional GRU, and combines the dynamic attention weighting mechanism to jointly model the non-linear relationship between turbulence, radiation, and phase change, and outputs an optimized fog area feature representation;

[0039] The physical constraint loss function module embeds physical constraints during the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, and optimizes the consistency between the data-driven features and the physical laws through adaptive weight allocation, improving the generalization ability of the model under complex terrain conditions.

[0040] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0041] 1. By designing a dual-branch heterogeneous network structure, the present invention respectively uses the Dense Block and U-Transformer modules to extract local details and large-scale evolution features for the different physical properties of the temperature-humidity phase state and the cloud-water phase state. The temperature-humidity phase state sub-module strengthens the fine extraction of local structures such as the top of the inversion layer and the humidity gradient, and the cloud-water phase state sub-module captures the multi-scale dynamic evolution during the processes of cloud-water condensation, sedimentation, and freezing. Overall, it makes up for the problem of insufficient fine-grained process characterization of traditional parameterization schemes under low turbulence intensity conditions.

[0042] 2. The present invention embeds multiple physical constraints such as mass conservation, momentum conservation, and visibility gradient matching during the training process. Through the joint optimization strategy, while improving the prediction accuracy, it ensures the consistency of the internal physical relationship between output variables, effectively enhancing the stability and reliability of the model under complex weather scenarios such as the development of the inversion layer and the intermittent outbreak of turbulence, and having strong business application value.

[0043] 3. Under complex terrain conditions, the present invention can accurately capture the multi-scale modulation effects of terrain on local radiative cooling, turbulence weakening, and fog generation and evolution. At the same time, by introducing a deep learning framework, it effectively reduces the dependence on large-scale and high-density observational data, reduces the sensitivity of numerical models to the quality of external input data, and improves the applicability of the model in data-sparse regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flowchart of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network of the present invention;

[0045] Figure 2 It is a structural diagram of the overall SMAP-Net network model of the present invention;

[0046] Figure 3 It is a structural diagram of the U-Transformer feature extraction network of the present invention;

[0047] Figure 4 It is a structural diagram of the ST-CAM feature fusion network of the present invention;

[0048] Figure 5 It is a comparison diagram of the correlation coefficient matrices of the SMAP-Net of the present invention and each model on multiple physical quantity pairs;

[0049] Figure 6 It is a spatial distribution diagram of the liquid water content of the SMAP-Net of the present invention and each model;

[0050] Figure 7 It is a scatter diagram of the correction accuracy of the liquid water path of the SMAP-Net of the present invention and each model;

[0051] Figure 8 It is a spatio-temporal comparison diagram of the visibility of the SMAP-Net of the present invention and different parameterization schemes. DETAILED DESCRIPTION OF THE INVENTION

[0052] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the application will be further elaborated in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments of other researchers in the field based on this embodiment belong to the protection scope of the present invention. At the same time, for the step numbers in the embodiments of the present invention, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0053] In an embodiment of the present invention, the flowchart of the method for revising the fog boundary layer parameterization scheme based on the multi-scale physical coupling network is as Figure 1 shown and includes the following steps:

[0054] S1. Generate multi-parameterized boundary layer simulation data using the Weather Research and Forecasting (WRF) model, which specifically includes the following processes:

[0055] Input the ERA5 reanalysis data (horizontal resolution 0.25°×0.25°, time resolution 6 hours) as the initial field and boundary conditions into the WRF model, and configure the WRF model parameters, including physical parameterization schemes (boundary layer schemes ACM2, YSU, QNSE) and grid settings (horizontal resolution 3 km, vertical resolution 50 layers, top pressure 50 hPa), to generate simulation results with a horizontal resolution of 3 km. The simulation data includes thermodynamic variables such as temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), air pressure (P), water substance variables such as cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), snow content (Qs), and dynamic field variables such as vertical velocity (W).

[0056] S2. Generate an initial feature tensor by processing the input data through feature encoding, and use the multi-head attention mechanism to screen key variables. The specific implementation includes the following steps:

[0057] S2.1. The input variables include temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), snow content (Qs), air pressure (P), and vertical velocity (W). Organize these variables into a three-dimensional spatio-temporal tensor with dimensions H×W×T×C, where H×W represents the spatial resolution, T represents the time step, and C = 9 represents the number of variable channels;

[0058] S2.2. Extract spatio-temporal local features through a parallel three-dimensional convolutional layer. The convolutional kernel size is 3×3×3, the stride is 1, and the padding is 1 to retain the spatial and time dimensions of the input tensor and generate an initial feature tensor , with the number of output channels being 64. Use the ReLU activation function to perform non-linear transformation on the features to enhance the model's expressive ability;

[0059] S2.3. Use the multi-head attention mechanism to screen the initial feature tensor to highlight the variables that have a greater impact on the evolution of the fog area (such as temperature gradient, humidity distribution). The calculation formula is as follows: where , , are the query, key, and value vectors respectively, is a learnable linear transformation matrix, and each matrix is responsible for transforming the input feature tensor Perform a linear transformation on the channel dimension, keeping the dimension unchanged and continuously updating it during the training process to optimize the attention calculation, realize the reweighting of information between channels and the feature subspace mapping, so that different variable combinations can adapt to the subsequent correlation modeling. is the dimension of the key vector, and the attention mechanism is configured with 8 heads to output the filtered feature tensor. to highlight the key variables that have a greater impact on the evolution of the fog area.

[0060] S3. Construct a multi-scale physical coupling network (SMAP-Net), extract the temperature-humidity phase state features and cloud-water phase state features through a dual-branch heterogeneous network structure. The overall structure of SMAP-Net is as Figure 2 shown, and it specifically includes the following processes:

[0061] S3.1. The input variables of the temperature-humidity phase state branch are temperature (T), relative humidity (RH), water vapor mixing ratio (Qv), and air pressure (P). Spatiotemporal local features are extracted through three-dimensional convolution (convolution kernel size is 3×3×3, stride is 1, padding is 1) to generate the initial feature tensor. where the number of output channels is 64.

[0062] S3.2. Adopt a 4-level Dense Block stacking structure, each level contains a bottleneck structure. The bottleneck structure includes in sequence: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, and 1×1×1 convolution for dimensionality increase. The features of the previous layer and the current layer are concatenated in channels through skip connections to output the feature tensor. where the number of output channels is 4×64 = 256 to enhance the feature reuse ability.

[0063] S3.3. Enhance the feature response of the inversion layer top and the humidity jump area through the channel-spatiotemporal hybrid attention (CSTA) mechanism. The calculation formula is as follows: where, represents the global average pooling result along the space-time dimension, is the learnable weight matrix used to model the dependencies between channels, is the Sigmoid activation function to generate the channel attention weights, represents element-wise multiplication, is the output feature tensor of the Dense Block, and the addition operation retains the original feature information to output the enhanced feature tensor. .

[0064] S3.4. The input variables of the cloud-water phase state branch are cloud water content (Qc), rain water content (Qr), ice crystal content (Qi), and snow content (Qs). Multi-scale features are extracted through a U-shaped encoding-decoding structure. The structure is as Figure 3As shown, the input data dimension is H×W×T×4, where the number of channels is 4;

[0065] S3.5. The encoder adopts 2-level downsampling and combines with the multi-scale self-adaptive position encoding MSPE block layer. Let the original three-dimensional coordinates of each position point be , where , are spatial coordinates, is the time index. For each dimension , different scale sets are selected, where , and the absolute position encoding is calculated: Among them, is the component of the coordinate on the dimension , is the single-dimension encoding vector, and the encoding vectors of each dimension are concatenated: Among them, is the complete absolute position encoding. For each scale , a learnable weight is introduced to adjust the importance of features at different scales; for any two positions and in the attention calculation, the coordinate difference is calculated: The coordinate difference is mapped to the relative position encoding through a lightweight MLP: Among them, matches the hidden dimension of the MSPE block. In each MSPE block layer, is linearly mapped and added to the input feature, and is used as the attention score bias term to enhance the multi-scale spatio-temporal modeling ability;

[0066] S3.6. The decoder fuses the low-level local features and high-level semantic information through 2-level upsampling (using a 3×3×3 convolution kernel with a stride of 2) and skip connections, and outputs the multi-scale cloud water phase state feature tensor .

[0067] S4. The dual-branch features are fused through the spatio-temporal coupling attention module (ST-CAM) to model the non-linear relationship between turbulence, radiation and phase change. The structure of ST-CAM is as Figure 4 shown, and the specific steps are as follows:

[0068] S4.1. The input feature tensor is the output of the temperature-humidity phase branch and the cloud water phase branch, with a dimension of H×W×T×128. A multi-resolution feature pyramid is constructed using 3D convolutional kernels with dilation rates of 1, 2, and 4 respectively (size 3×3×3, stride 1, padding same), and the output channel numbers are 64, 128, and 256 respectively. They are fused into a unified feature tensor through 1×1×1 convolution to expand the receptive field and capture multi-scale spatio-temporal patterns;

[0069] S4.2. Model the lag effect of the development of the temperature inversion layer along the time axis through a bidirectional GRU. The input feature tensor is unfolded into a sequence along the time axis . The bidirectional GRU contains 2 layers, with the hidden state dimension of each layer being 128, the activation function being tanh, and the hidden state update formula being: , where is the update gate, is the reset gate, , , , , , are learnable weight matrices, , , are bias terms, is the Sigmoid activation function, is the element-wise multiplication, is the unidirectional hidden state. The bidirectional GRU generates the final hidden state through forward and backward calculations to enhance the ability of temporal dynamic modeling.

[0070] S4.3. Use the spatial self-attention mechanism to calculate the correlation weights between grid points and generate a dynamic attention map. The calculation formula is as follows: where , , are the query, key, and value vectors respectively, , , are linear transformation matrices. Each matrix linearly transforms the number of channels of the input while keeping the number of channels unchanged, and re-encodes the semantic representation of each grid point in different feature subspaces to provide an adapted feature subspace mapping for subsequent attention score calculation. is the key vector dimension. The output attention-weighted feature tensor is multiplied element-wise with to generate the final fused feature tensor .

[0071] S5. Embed a physical constraint loss function during the decoding stage to optimize the correction results of the boundary layer variables, specifically including the following steps:

[0072] S5.1. The pixel-level reconstruction loss uses weighted mean squared error (WMSE) to constrain the consistency between the correction field and large eddy simulation (LES) data, defined as: where, represents the predicted correction field of the model at position ( ), is the true value of the LES simulation, is the dynamic weight, and the calculation formula is: where, is the terrain height at position , is the fog top height, is the standard deviation, and the weight design highlights the prediction accuracy in the area near the fog top;

[0073] S5.2. The mass-momentum conservation term strengthens physical self-consistency by minimizing the residual of the Navier-Stokes equation, defined as: where, is the air density, is the three-dimensional wind speed vector, is the air pressure, is the acceleration due to gravity, represents the divergence of the mass flux, constraining the continuity equation, is the material derivative of the wind speed, and combines the pressure gradient and gravity terms to reflect momentum conservation , are hyperparameters determined by grid search and cross-validation;

[0074] S5.3. The visibility gradient matching term maximizes the similarity between the visibility and surface temperature features through a contrastive loss, defined as: where, is the feature vector of the visibility field, is the feature vector of the surface temperature field, is the negative sample feature vector, is the cosine similarity function, is the temperature parameter, and the feature vectors are extracted by a three-layer convolutional neural network (CNN), with each layer using a 3×3 convolutional kernel and the number of channels being 64, 128, and 256 respectively;

[0075] S5.4. The total loss function is the weighted sum of each part: where, and are adaptive weight parameters dynamically optimized by a small multi-layer perceptron (MLP). The MLP contains two fully connected layers, and the input is the current training epoch , , , the output is and , and the optimization goal is to minimize the prediction error on the validation set.

[0076] S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content and visibility, and improve the simulation accuracy of the liquid water path (LWP) and liquid water content (LWC) in the fog area.

[0077] The present invention also includes a multi-scale physical coupling network (SMAP-Net) model, and the multi-scale physical coupling network (SMAP-Net) model includes a dual-branch feature extraction module, a spatio-temporal coupling attention module and a physical constraint loss function module;

[0078] The dual-branch feature extraction module respectively extracts the temperature-humidity phase state features and the cloud water phase state features through a dual-branch heterogeneous network structure. Among them, the temperature-humidity phase state branch uses the Dense Block and CSTA mechanisms to capture the multi-scale features of temperature and humidity, and the cloud water phase state branch uses the U-Transformer module to extract the spatial distribution features of the cloud water content;

[0079] The spatio-temporal coupling attention module fuses the dual-branch features output by the multi-scale physical coupling network module, performs spatio-temporal encoding using 3D convolution, models the temporal dependence relationship through bidirectional GRU, and combines the dynamic attention weighting mechanism to jointly model the non-linear relationship between turbulence, radiation and phase change, and outputs an optimized fog area feature representation;

[0080] The physical constraint loss function module embeds physical constraints during the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, and optimizes the consistency between the data-driven features and the physical laws through adaptive weight allocation, and improves the generalization ability of the model under complex terrain conditions.

[0081] In addition, to systematically evaluate the performance advantages of the multi-scale physical coupling network (SMAP-Net) proposed by the present invention in the multi-physical quantity collaborative correction in the radiation fog boundary layer parameterization, the present invention comprehensively compares the performance of SMAP-Net with traditional boundary layer parameterization schemes and existing deep learning models in complex fog area environments. Figure 5 This is the correlation coefficient matrix comparison chart of SMAP-Net of the present invention and each model for multi-physical quantity pairs. The results show that SMAP-Net has the highest consistency with the LES benchmark value, and the average deviation of all variable pairs is only 0.03, highlighting its superior ability to capture the collaborative interaction between thermodynamic and microphysical variables. To further evaluate the physical consistency of each model in fog area simulation. Figure 6The spatial distribution map of the liquid water content of the SMAP-Net of the present invention and each model is shown. The results show that the SMAP-Net can accurately reproduce the distribution characteristics of the LWC in the fog area. Especially in the complex terrain area, its simulation results are highly consistent with the LES true value.

[0082] Finally, a typical strong fog event is selected for case analysis in the present invention. Figure 7 This is the scatter plot of the liquid water path correction accuracy of the SMAP-Net of the present invention and each model, which is used to evaluate the deviation of each model compared with the LES true value. From the results, the SMAP-Net highly coincides with the reference line at most points, and its root mean square error of the liquid water path is significantly better than the traditional boundary layer parameterization scheme. Figure 8 This is the spatio-temporal comparison map of visibility between the SMAP-Net of the present invention and different parameterization schemes. The results show that the SMAP-Net model can accurately reproduce the fog outbreak process, with a low error from the observation time. Thanks to its dynamic learning ability for the non-equilibrium state of radiative cooling, the fog area boundary is highly coupled with the terrain undulation. Especially in the karst basin and narrow valley, it shows the fog patch distribution at the sub-kilometer scale, which has a significant improvement compared with the traditional scheme.

[0083] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for correcting the parameterization scheme of the fog boundary layer based on a multi-scale physical coupling network, characterized in that: The following steps are involved: S1. Generate multi-parameterized boundary layer simulation data using the numerical weather forecast model WRF. The input data include thermodynamic variables, water material variables and dynamic field variables. S2, the input data is processed by feature encoding to generate the initial feature tensor, and the key variables with greater weight influencing the evolution of the fog area are screened out by using the multi-head attention mechanism; S3. Construct a multi-scale physical coupling network SMAP-Net, and extract temperature and humidity phase characteristics and cloud water phase characteristics of different scales through a dual-branch heterogeneous network structure; S4, through the spatiotemporal coupled attention module ST-CAM to fuse dual-branch features, three-dimensional convolutional spatiotemporal coding, bidirectional GRU temporal modeling and dynamic attention weighting, the nonlinear relationship between turbulence, radiation and phase change is jointly modeled; S5. During the training optimization process, physical constraint loss functions are introduced, including the mass-momentum conservation equation and visibility gradient matching terms. The data-driven features and physical laws are coordinated and optimized through adaptive weight allocation to correct boundary layer variables. S6. Output the corrected boundary layer variables, including temperature, humidity, cloud water content and visibility, to improve the simulation accuracy of liquid water path LWP and liquid water content LWC in the fog area.

2. According to the method for correcting the parameterization scheme of fog boundary layer based on multi-scale physical coupling network according to claim 1, it is characterized in that: In step S2, the specific implementation of the encoding stage includes: S2.

1. Input variables include temperature T, relative humidity RH, water vapor mixing ratio Qv, cloud water content Qc, rain water content Qr, ice crystal content Qi, snow content Qs, air pressure P, and vertical velocity W. The input data are organized into a three-dimensional space-time tensor with dimensions H×W×T×C, where H×W represents spatial resolution, T represents time step, and C represents the number of variable channels. S2.

2. Extract spatiotemporal local features through a parallel three-dimensional convolutional layer, where the convolution kernel size of the three-dimensional convolutional layer is 3×3×3, the stride is 1, and the padding is 1; generate an initial feature tensor ,in Indicates the number of output channels and uses the ReLU activation function for nonlinear transformation; S2.

3. Using the multi-head attention mechanism to the initial feature tensor To screen, the calculation formula is as follows: in, , , are query, key and value vectors respectively, is a learnable linear transformation matrix, each of which is responsible for transforming the input feature tensor The channel dimension is linearly transformed, the dimension is kept unchanged and continuously updated during the training process to optimize the attention calculation, realize the re-weighting of the information between channels and the mapping of feature subspaces, so that different variable combinations can adapt to the subsequent correlation modeling. is the dimension of the key vector, and the attention mechanism is configured as Head, of which It is an adjustable hyperparameter and outputs the filtered feature tensor , in order to highlight the key variables that have a greater impact on the evolution of the fog area.

3. The method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network according to claim 1 is characterized in that: In step S3, the specific implementation of the temperature and humidity phase state branch includes: S3.

1. Input variables are temperature T, relative humidity RH, water vapor mixing ratio Qv and air pressure P. Local spatiotemporal features are extracted through three-dimensional convolution. The convolution kernel size of the three-dimensional convolution is 3×3×3, the stride is 1, and the padding is 1. The initial feature tensor is generated. , where the number of output channels is 64; S3.2, adopts a 4-level Dense Block stacking structure, each level contains a bottleneck structure, the bottleneck structure includes: 1×1×1 convolution for dimensionality reduction, 3×3×3 convolution for feature extraction, 1×1×1 convolution for dimensionality increase, and the previous layer features are spliced ​​with the current layer features through jump connections to output feature tensors , where the number of output channels is 4×64=256 to enhance feature multiplexing capability; S3.

3. Enhance the characteristic response of the top of the inversion layer and the humidity jump zone through the channel-time-space hybrid attention CSTA mechanism. The calculation formula is as follows: in, represents the global average pooling result along the space-time dimension, is a learnable weight matrix used to model the dependencies between channels. For the Sigmoid activation function, generate channel attention weights, represents element-wise multiplication, Output feature tensor for Dense Block, the addition operation retains the original feature information, and outputs the enhanced feature tensor .

4. The method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network according to claim 1 is characterized in that: In step S3, the U-Transformer module of the cloud-water phase branch includes: S3.4, the input variables are cloud water content Qc, rain water content Qr, ice crystal content Qi and snow content Qs. Multi-scale features are extracted through the U-type encoding-decoding structure. The input data dimension is H×W×T×4, where the number of channels is 4; S3.5, the encoder uses 2-level downsampling and combines the multi-scale adaptive position encoding MSPE block layer, assuming that the original three-dimensional coordinates of each position point are ,in , is the spatial coordinate, is the time index, for each dimension , select different scale sets ,in Is a positive integer used to control the number of frequency resolution levels of the encoding and calculate the absolute position encoding: in, For coordinates In Dimension The weight on For a single-dimensional encoding vector, concatenate the encoding vectors of each dimension: in, For the complete absolute position encoding, for each scale Introducing learnable weights , used to adjust the importance of features of different scales; for any two positions in the attention calculation and , calculate the coordinate difference: The coordinate difference Mapped to relative position encoding via lightweight MLP: The relative position encoding The dimension matches the hidden dimension of the MSPE block. In each MSPE block layer, the absolute position of each position is encoded The relative position is encoded by adding it to the input feature after linear mapping As a bias term in the calculation of attention weights, it is used to adjust the attention strength between different positions, thereby enhancing the modeling ability of multi-scale spatiotemporal relationships; S3.6, the decoder uses a 3×3×3 convolution kernel with a stride of 2 and a jump connection to fuse low-level local features with high-level semantic information and output a multi-scale cloud water phase feature tensor .

5. The method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network according to claim 1 is characterized in that: In step S4, the implementation of the spatiotemporal coupled attention module ST-CAM includes: S4.

1. The input feature tensor is the output of the temperature and humidity phase branch and the cloud water phase branch, with a dimension of H×W×T×C. A multi-resolution feature pyramid is constructed using a three-dimensional convolution kernel with expansion rates of 1, 2, and 4. The size of the three-dimensional convolution kernel is 3×3×3 3, the stride is 1, and the padding is the same. The number of output feature channels is set to , , ,in < < , to achieve dimensionality increase, the features of the three scales are fused into a unified feature tensor through a 1×1×1 convolution layer , the number of channels is , in order to expand the receptive field of the model and capture the multi-scale spatiotemporal evolution patterns, and improve the ability to model the boundary layer variables in fog areas; S4.

2. Model the lag effect of the development of the inversion layer along the time axis through a bidirectional GRU, and input the feature tensor Expand into a sequence along the time axis , the bidirectional GRU contains 2 layers, each layer has a hidden state dimension of 128, the activation function is tanh, and the hidden state update formula is: in, To update the gate, To reset the gate, , , , , , is the learnable weight matrix, , , is the bias term, is the Sigmoid activation function, is element-wise multiplication, It is a unidirectional hidden state. The bidirectional GRU generates the final hidden state through forward and backward calculations. , enhance the timing dynamic modeling capabilities; S4.

3. Use the spatial self-attention mechanism to calculate the association weights between grid points and generate a dynamic attention map. The calculation formula is as follows: Among them, SA represents the spatial attention mechanism, which is used to calculate the attention weight based on the feature similarity between each grid point. , , are query, key and value vectors respectively, , , is a linear transformation matrix, each matrix is ​​input The number of channels is linearly transformed to keep the number of channels unchanged, and the semantic representation of each grid point is re-encoded in different feature subspaces to provide an adaptive feature subspace mapping for subsequent attention score calculation. is the key vector dimension, outputs the attention-weighted feature tensor, and then Multiply element by element to generate the final fused feature tensor .

6. The method for correcting the parameterization scheme of the fog boundary layer based on the multi-scale physical coupling network according to claim 1 is characterized in that: In step S5, the physical constraint loss function includes: S5.

1. The pixel-level reconstruction loss uses the weighted mean square error (WMSE) to constrain the consistency between the correction field and the large eddy simulation (LES) data, which is defined as: in, Represents the position ( )'s prediction correction field, is the true value of LES simulation, is the dynamic weight, and the calculation formula is: in, For location The terrain height, is the fog top height, is the standard deviation, and the weight design weights the deviation between the terrain height and the fog top height in the form of a Gaussian function, thereby enhancing the error constraint of the key layer near the fog top in the loss function and improving the simulation accuracy of the key area; S5.

2. The mass-momentum conservation term enhances physical self-consistency by minimizing the residual of the Navier-Stokes equations and is defined as: in, is the air density, is the three-dimensional wind speed vector, is the air pressure, is the acceleration due to gravity, represents the divergence of the mass flux and is used to constrain the continuity equation, represents the material derivative of wind speed, It represents the balance relationship between inertial force, pressure gradient force and gravity in the conservation of momentum. , To adjust the hyperparameters of the two weights, grid search and cross validation were used; S5.

3. The visibility gradient matching term uses a contrast loss function to maximize the similarity between visibility characteristics and surface temperature characteristics to enhance the model's sensitivity to radiation cooling and fog layer changes. The loss function is defined as: in, is the eigenvector of the visibility field, is the characteristic vector of the surface temperature field, is the negative sample feature vector, is the cosine similarity function, is the temperature parameter, and the feature vector is extracted by a three-layer convolutional neural network (CNN). Each layer uses a fixed-size 3×3 convolution kernel, and the number of output channels increases layer by layer to capture spatial patterns and semantic information at different levels; S5.

4. The total loss function is the weighted sum of each part: in, and The adaptive weight parameters are dynamically optimized by a small multi-layer perceptron MLP; the MLP contains two fully connected layers, and the input is the current training round , , , the output is and , the optimization goal is to minimize the prediction error on the validation set.

7. The method for correcting the fog boundary layer parameterization scheme based on a multi-scale physical coupling network according to claim 1 is characterized in that: It also includes a multi-scale physical coupling network model, wherein the multi-scale physical coupling network model includes a dual-branch feature extraction module, a spatiotemporal coupling attention module, and a physical constraint loss function module; The dual-branch feature extraction module extracts temperature and humidity phase characteristics and cloud water phase characteristics respectively through a dual-branch heterogeneous network structure. The temperature and humidity phase branch uses Dense Block and CSTA mechanisms to capture the multi-scale characteristics of temperature and humidity, and the cloud water phase branch uses the U-Transformer module to extract the spatial distribution characteristics of cloud water content; The spatiotemporal coupled attention module integrates the dual-branch features output by the multi-scale physical coupling network module, uses three-dimensional convolution for spatiotemporal encoding, models temporal dependencies through bidirectional GRU, and combines the dynamic attention weighting mechanism to jointly model the nonlinear relationship between turbulence, radiation and phase change, and outputs the optimized fog area feature representation; The physical constraint loss function module embeds physical constraints in the model training process, combines the mass-momentum conservation equation and the visibility gradient matching term, optimizes the consistency between data-driven features and physical laws through adaptive weight allocation, and improves the generalization ability of the model under complex terrain conditions.

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